{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "134e7f9d",
   "metadata": {},
   "source": [
    "# Demo 2: Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2571d531",
   "metadata": {},
   "source": [
    "Initialize KAN and create dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2075ef56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1000, 2]), torch.Size([1000, 1]))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from kan import *\n",
    "# create a KAN: 2D inputs, 1D output, and 5 hidden neurons. cubic spline (k=3), 5 grid intervals (grid=5).\n",
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "\n",
    "# create dataset f(x,y) = exp(sin(pi*x)+y^2)\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2)\n",
    "dataset['train_input'].shape, dataset['train_label'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c6add1d",
   "metadata": {},
   "source": [
    "Plot KAN at initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ac76f858",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot KAN at initialization\n",
    "model(dataset['train_input']);\n",
    "model.plot(beta=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8071b133",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if you want to add variable names and title\n",
    "model.plot(beta=100, in_vars=[r'$\\alpha$', 'x'], out_vars=['y'], title = 'My KAN')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddf67e30",
   "metadata": {},
   "source": [
    "Train KAN with sparsity regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "97111d75",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.56e-01 | test loss: 1.31e-01 | reg: 2.07e+01 : 100%|██| 20/20 [00:12<00:00,  1.64it/s]\n"
     ]
    }
   ],
   "source": [
    "# train the model\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=10.);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f30c3ab",
   "metadata": {},
   "source": [
    "$\\beta$ controls the transparency of activations. Larger $\\beta$ => more activation functions show up. We usually want to set a proper beta such that only important connections are visually significant. transparency is set to be ${\\rm tanh}(\\beta |\\phi|_1)$ where $|\\phi|_1$ is the l1 norm of the activation function. By default $\\beta=3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3f95fcdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6383a22f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9f6ff7e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61d537b7",
   "metadata": {},
   "source": [
    "After purning, \"mask=True\" will remove all connections that are connected to unsignificant neurons. The insignificant neurons themselves are still visualized. If you want those neurons to be removed as well, see below. Insignificant/Significant neurons are defined based on l1 norm of its incoming and outgoing functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1269a698",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2249bb17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+/5UodczucfTfNbsoF0EQMGfOnAY9d+7cuTZ90stSOGYNw3F7surqanz99dcYPnw4OnXqhOTkZAwePLhBr6WUMXsYR/9ds4sT+oBjvx/cUjhmDcNxe7irV68iISEB8fHxKCoqQr9+/aDT6TBu3DiYzeZ6jRkAaDQaXLlyxaHH7Ekc+XfNLmYuAODu7o709HQIgvDEKbhKpYIgCPjqq69s/gdgSRyzhuG4/X+iKOL777/H+PHj8cwzz+DDDz9EaGgoCgoKcPDgQURERMDFxaVeY3bvL25PT89Gn9S2dw79u2blHQEara578GRlZckd1WZwzBpGyeNWWloqrlmzRuzSpYsIQOzSpYu4Zs0asbS09LHPq+uYffHFF+Kzzz4rdujQQSwsLLTSd2W7HPF3ze7KRRRFsaSkRIyNjRV9fHx+9UPw8fERY2Njn3gAKBHHrGGUNm4FBQXizJkzRVdXV7FJkybiq6++Kn733XdibW1tnV+jrmN26dIlsWPHjmK7du3Ec+fOWepbshuO9rtmN+dcHkYURdy6dQvl5eVo3rw5PDw8bP4kl9w4Zg3jyONmNpuxfft26PV6HDp0CE8//TRee+01zJgxA23btm3w69ZlzK5evYqgoCAUFxdj37598PPza+y3Y/cc5XfNrsuFiBqusLAQ8fHx2LBhA4qLizFs2DBotVq88soraNLEevcR/PnnnzFs2DBcvnwZ2dnZCAgIsNrXJsthuRApSE1NDfbs2QODwYA9e/agRYsWmDZtGmbNmoU//OEPsuUqKSlBcHAwzp8/j8zMTPTp00e2LCQNlguRAty4cQMbN25EXFwcLl26hN69e0On02HChAlwdXWVOx4AoKysDKGhoThx4gQyMjIwaNAguSNRI7BciByUKIo4ePAg9Ho9vvzyS6jVakycOBFarRaBgYFyx3uoyspKhIWF4dChQ9i5c+f92yST/WG5EDmY8vJybN68GXq9HqdPn0bHjh2h1WoxdepUm98yBABMJhPGjRuH/fv3Iz09HaGhoXJHogZguRA5iLNnz8JgMCApKen+DECn02Ho0KEN2vtLTnfu3MHEiROxa9cupKWlYezYsXJHonpiuRDZsbt37+Lrr7+GXq/H3//+d7Rp0wbR0dGIjo5G+/bt5Y7XKFVVVZgyZQq2bduGxMRETJo0Se5IVA/We78hEUnmP//5Dz777DMkJCTg+vXrGDx4MLZu3YpRo0ahadOmcseThJOTE5KTk+Hi4oLIyEiYzWZMnz5d7lhURywXIjtRW1uL7Oxs6PV67Nq1C25ubpg8eTK0Wi26du0qdzyLUKvVSEhIgIuLC2bMmAGz2YyYmBi5Y1EdsFyIbFxxcTG++OILGAwGXLx4Ec8//zwMBgPCw8MbfcMpe6BSqbB+/XpoNBrMnj0bJpMJCxYskDsWPQHLhcgGiaKIvLw86PV6bNmyBaIoYvz48UhOTkbfvn3tcjuQxhAEAR9//DFcXV2xcOFCGI1GLF++XHHjYE9YLkQ2xGg0Ii0tDXq9Hvn5+XjuueewYsUKREVFwcvLS+54shIEAe+++y40Gg3eeustmEwmvP/++ywYG8VyIbIB586dg8FgQGJiIm7fvo0//vGPyMjIQHBwMNRqtdzxbMqbb74JV1dXvPHGGzCZTPj0009ZMDaI5UIkk+rqauzcuRN6vR779+9Hq1atMGvWLMycORMdOnSQO55Ne/311+Hi4gKtVguTyQSDwWB31/I4OpYLkZVduXIFn3/+OT777DNcuXIF/fv3R0pKCsaNGwdnZ2e549mNWbNmQaPRICoqCmazGRs2bLDqbs70ePxJEFmBKIr47rvvoNfrsWPHDri4uCAiIgJarRbPP/+83PHs1pQpU+Di4oJJkybBbDYjJSUFTk5Ocsci8Ap9IosqLS1FUlISDAYDfvzxR3Tt2hU6nQ4RERFo0aKF3PEcxo4dOzB+/HiEhIRg27ZtnAHaAJYLkQXk5+fDYDAgNTUVd+/exZgxY6DT6TBo0CCefLaQzMxMjB49GoMGDcLXX39tM7cSUCqWC5FEzGYztm3bBr1ejyNHjqBdu3b3bxfcpk0bueMpQk5ODsLCwhAYGIhvv/1WEReZ2iqWC1EjXbx4EXFxcdi0aROKi4sxfPhw6HQ6hIaG8gSzDA4cOICQkBD4+fndv9smWR/LhagBampqsHv3buj1emRmZqJly5aIiorCa6+9Bl9fX7njKV5eXh6Cg4Ph7e2NrKwseHp6yh1JcVguRPVw/fp1bNiwAfHx8fjPf/6DwMDA+7cL1mg0csejXzh58iSGDRuGNm3aIDs7G61bt5Y7kqKwXIieQBRF5ObmQq/XIz09HWq1GuHh4dBqtejdu7fc8egx/vnPf2Lo0KF46qmnsH//fjz99NNyR1IMlgvRI5SVlSElJQUGgwFnzpyBr68vdDodpkyZgpYtW8odj+rowoULGDp0KJo0aYKcnBw8++yzckdSBJYL0W+cPn0aBoMBycnJMJlMGDlyJLRaLYYMGcItRuzUpUuXMGTIEFRVVSEnJwcdO3aUO5LDY7kQ4b/3bP/qq6+g1+uRm5uLNm3aYObMmYiOjka7du3kjkcSKCoqQlBQEG7fvo19+/Y57A3WbAXLhRTt0qVL928XfOPGDbz00kvQ6XQYOXIktxFxQDdu3EBQUBCuXbuG7Oxsbr1jQSwXUpza2lrs3bsXer0eGRkZcHNzw9SpUzFr1ix06dJF7nhkYcXFxQgODkZhYSGysrIQGBgodySHxHIhxbh58yY2bdqEuLg4FBYWokePHtDpdAgPD0ezZs3kjkdWdO+eOadPn8bu3bsxcOBAuSM5HJYLOTRRFHHkyBEYDAZs3boVoihiwoQJ0Ol06NOnD/f5UrCKigq88sorOHr0KL799lsMGTJE7kgOheVCDqmysvL+7YILCgrQoUMHaLVaTJs2Da1atZI7HtkIk8mE0aNH429/+xu++uorhISEyB3JYbBcyKH8+OOP928XXFZWhpdffhlarRbBwcF8GzE91J07dzBhwgTs3r0bW7duxejRo+WO5BBYLmT3qqqq8M0338BgMCAnJwdeXl6YMWMGZs6cieeee07ueGQHqqqqEBERgfT0dKSkpOBPf/qT3JHsHrdsJbtVVFR0/3bBV69excCBA5GamooxY8bwZlFUL05OTkhNTcX06dMRHh4Os9mMqVOnyh3LrrFcyK6IooicnBzo9Xp888030Gg0iIyMhFarhb+/v9zxyI6p1Wps3LgRLi4umDZtGkwmE7Rardyx7BbLhexCSUkJEhMTERcXh3PnzqFbt25Ys2YNIiIi8NRTT8kdjxyESqWCwWCAi4sLdDodzGYz3njjDblj2SWWC9m048eP379dcHV1NcaOHYvPP/8cAwcO5NuIySIEQcCnn34KV1dXzJs3D0ajEW+99ZbcsewOy4Vsjslkun+74KNHj6J9+/ZYtmwZpk+fzntykFUIgoD3338frq6uWLZsGUwmE959913+QVMPLBeyGRcuXLh/u+Bbt25hxIgR+OabbxAaGgq1Wi13PFKgZcuWwcXFBQsXLoTJZMLHH3/MgqkjlgvJqrq6GhkZGTAYDMjKyoKHh8f92wVzW3SyBQsWLIBGo8Hs2bNhMpmwbt06XjNVBywXksW1a9fu3y74p59+Qp8+fZCYmIhXX32VtwsmmxMTEwONRoMZM2bAZDIhISGBs+knYLmQ1YiiiB9++OH+7YKdnJwwadIkaLVa9OzZU+54RI8VFRUFFxcXTJ48GWazGUlJSbwtw2OwXMjiysrKkJycDIPBgLNnz6JTp074+OOPMWXKFLi7u8sdj6jOwsPD4ezsjIkTJ+LOnTtIS0vjBbuPwO1fyGJOnTp1/3bBZrMZo0aNgk6nw0svvcSTomTXMjIyMHbsWAwZMgTp6elcyn0IlgtJ6s6dO0hPT4der8eBAwfw+9//HjNnzsSMGTPw9NNPyx2PSDL79+9HWFgY+vbti507d/KeQL/BciFJ/Pvf/0Z8fDw2bNiAn3/+GUOHDoVWq0VYWBjXpclh/fDDDwgNDUX37t2xe/du7hbxCywXapRr164hOjoaGRkZeOqpp+7fLrhz585yRyOyiiNHjmDEiBHw9fVFZmYmPDw85I5kE1gu9FArV66UZCNIk8kEFxeXh55juXnzJqKjoxv9NYgsQapj4FHMZjMqKioc9hjgu8Xooc6ePYulS5c26jU2b96M2NhYdO7cGZs2bXrguoCJEyc67IFF9u/s2bNYtGiRRa5nuX79OkaPHo1nn33WYY8BXmZKDyUIApycnBr878yZM5g5cyYWL16MM2fOYPbs2Q88hsiWCYKASZMmQaVSNepYeNi/adOmwdvbW+5v0aJYLiQ5URQxbNgwrF69GhMmTEBOTg42bNgAs9ksdzSiejlz5gyWLFki6WuKooh9+/YhLi5O0te1NSwXklxOTg6MRiO0Wi0EQYCXlxdeeOEFzJ07V+5oRPWSnZ2NTz75BFKemjYajQDg8BcQs1xIUqIoYty4cUhISPjVSfyvv/4aCQkJkh6kRJbWvn17qNVqnD17VrLXXLVqFbp06eLwFxKzXEhSZWVlKC0txcSJE3/18bZt20p+kBJZmiAImDt3LiIiIiR7zU8++QQGg0Gy17NVLBeSVHR0NIKCgh74q0wQBCxZsgTjxo2TKRlRw6xcuRInT56UZNYtiiKMRiP+53/+R4Jkto3lQpIRRRHbt29HSkrKQz+/fPlynDt3DrW1tVZORtRwrq6uAP57zVZj3bp1CwAUcT8Yx/8OyWqKiooAAL/73e8e+vmmTZvC3d0d27dvt2YsokYRBAEdO3bEX//610a/1ooVK9C7d28JUtk+lgtJJjIyEuHh4Y89UfnFF19gxowZPLFPdmX9+vVYtWpVo1/n888/x9q1ayVIZPt4hT5JQhRFfP/99ygpKXns48LCwlBRUYFLly5ZKRlR4wUFBaGiogKiKDb4XV6iKMJsNuOFF16QOJ1t4syFJHH16lUIgoAWLVo89nGCIGDRokUICQmxUjKixrt3juRJfzw9jpLOtwAsF3qMysrKOj922rRpGDduXJ3+qnvvvffw4YcfNiYakdW98MILWL58eYOf//bbbytm1gKwXOgxBg0ahDt37jzxcaIoYu/evXXezkKtVmPkyJGNjUdkVXFxcUhISGjw8xMSEhRxfcs9LBd6JI1Gg6lTpz7xcdevX4cgCGjZsqXlQxHJpEePHrh7926D3owiiiLu3r2LgIAACySzTSwXeqRdu3Zhy5YtT5y9TJ48Ga+++qrDb2dByiYIApydnZGXl1fv5x45cgTOzs6KOkZYLvRI7u7u6NWrF15//fVHPkYURWRnZzv8Dq9EALBkyRJMnjy53s+LjIzEW2+9ZYFEtovlQo+1c+dOxMfHP3Ip4MSJE3BycnL4HV6JAGDp0qU4d+5cvZbGamtrceHCBSxevNiCyWwPy4Ueq23btmjRogW2bNny0M+PGTMGK1euVNR0n5TL2dkZ7u7u2LZtW52fs27dOrRt2xZNmza1YDLbw3KhxxIEAdu2bXvoVfXl5eX497//jQULFsiUjsj6tmzZgqioqDrNXqqqqjB//nzs2rXLCslsC8uFnigoKAhVVVU4fPjw/Y+Joojx48cjNDQUTZpwowdSjuHDh6Np06bYsGHDYx9XW1uLiIgI9OjRQ1HvEruH/yvQEwmCgPj4eISGhuLmzZtQqVT4xz/+gaysLJSVlckdj8iqBEFAVlYWBgwYgICAAPTs2fNXy8I1NTUoLCzEypUrcejQIZw6dUqRy8acuVCdTJ06Fe7u7oiJiUFubi4GDx6MVatWwc3NTe5oRFYXGBiIDz/8EEFBQfjggw9w6NAhHD16FElJSQgPD8eQIUNgNBpx+PBhxb7ZhTMXeqTfrinn5uZi/PjxmD59OmbOnIkFCxZwd2NyaI/7/Z43bx66dOmCtWvXIjk5GaIoolWrVnjxxRexePFidO/eHWq1WrHHCMuFHqpVq1bYsWPHAx+fPXs2ysvLH/n5+ujRo0ejnk9kSXX9HY+KisLt27chiiKaN28OZ2dnXLp0qU47fzvyMSCISq1Veqzq6mqLfw1BEKBWqy3+dYgagsdA47BciIhIcjyhT43yv//7v9BoNPjxxx/ljkIki7t376JXr17o2rUrTCaT3HFsBs+5UINlZ2djzZo1iI2NRefOneWOQySLd999F6dOncLhw4eh0WjkjmMzuCxGDVJSUgJ/f3907twZe/fuVczd9Yh+6fDhwxgwYADeeeedRt1IzBGxXKhBJk2ahIyMDJw+fRrt27eXOw6R1VVWVqJHjx7w9PREbm4ud6r4DY4G1du2bduQmpqKlJQUFgsp1sKFC1FUVISMjAwWy0Nw5kL1cuXKFfj5+SEoKAhbt25V5LYWRJmZmQgJCcH69euh0+nkjmOTWC5UZ6IoIiQkBKdOncLp06fh6ekpdyQiqysuLoa/vz+6d++OPXv28A+sR+BcjuosLi4OWVlZ2LNnD4uFFEkURWi1Wty5cwcbN25ksTwGy4Xq5F//+hfmz58PrVaLESNGyB2HSBapqan48ssvsXXrVvz+97+XO45N47IYPVF1dTUGDBiAkpISFBQUoFmzZnJHIrK6n376Cf7+/ggNDcXmzZvljmPzOHOhJ/rggw9w7NgxHDhwgMVCilRbW4tp06bBzc0N69atkzuOXWC50GMdP34cK1euxJtvvom+ffvKHYdIFuvWrcP+/fuRnZ2Nli1byh3HLnBZjB7JZDKhZ8+ecHV1xeHDh+Hk5CR3JCKr++c//4mePXsiOjoaa9askTuO3WC50CO9/vrriI+Px/Hjx9G1a1e54xBZXVVVFfr164fKykocP34crq6uckeyG1wWo4fav38/YmNjsXr1ahYLKdZf/vIXnDx5EocOHWKx1BNnLvSA0tJS+Pv7o1OnTtyUkhTryJEjGDBgAN5++228/fbbcsexOywXekBERAR27drFTSlJsSorKxEQEICWLVviwIED3DusAThi9CtffvklNm/ejOTkZBYLKdaiRYtw+fJl7Nq1i8XSQJy50H1Xr16Fn58fhgwZgm3btnFrC1KkrKwsjBgxAuvWrUNMTIzccewWy4UA/HfPpNDQUBQUFODMmTPcO4wU6datW/Dz84O/vz8yMzP5B1YjcL5HAID4+Hjs2bMHu3fvZrGQYul0OpjNZm5KKQGWC+H8+fOYP38+Zs2ahZCQELnjEMkiLS0NW7duxZYtW/D000/LHcfucVlM4aqrqzFw4EAUFxfjxIkT3DuMFOny5cvw9/dHSEgIUlNT5Y7jEDhzUbgPP/wQeXl53JSSFOveppTNmjXD+vXr5Y7jMFguCnb8+HGsWLECS5cu5aaUpFjr16/Hvn37sHfvXm5KKSEuiymUyWRCr1694OLigsOHD6Np06ZyRyKyuh9//BEBAQGYMWMG1q5dK3cch8JyUag33ngDBoMB+fn53DuMFKmqqgr9+/dHeXk58vPzuXeYxLgspkA5OTlYvXo1Pv30UxYLKdZ7772HgoICbkppIZy5KExpaSm6d+8OX19fZGdnc1NKUqSjR4+if//+WL58Of785z/LHcchsVwUJjIyEjt37sTp06fxzDPPyB2HyOqMRiMCAgLQokULHDhwgDfBsxAuiynI9u3bkZKSgqSkJBYLKdaiRYvw008/YefOnSwWC+LMRSHubUr50ksv4csvv+TWFqRIe/fuRXBwMNauXYvZs2fLHcehsVwU4N6mlPn5+Thz5gxatWoldyQiq7t16xb8/f3RrVs3ZGZm8nyjhXFZTAE+++wz7NmzB7t27WKxkGLFxMTAaDRi06ZNLBYrYLk4uAsXLmDevHl47bXXEBoaKnccIlls2bIFW7ZsQVpaGjeltBIuizmw6upqDBo0CDdu3MCJEyfg5uYmdyQiqysqKoKfnx9GjBiBtLQ0ueMoBmcuDmzVqlU4cuQIcnNzWSykSPc2pXR1deWmlFbGcnFQ+fn5eOedd7BkyRL069dP7jhEstDr9cjOzkZWVhY8PDzkjqMoXBZzQGazGb169YKzszM3pSTFOnfuHAICAhAVFYV169bJHUdxWC4OaN68edDr9Th+/Di6desmdxwiq6uqqsKAAQNw+/ZtFBQUcO8wGXBZzMF89913+PTTT/HJJ5+wWEix3n//feTn5+PgwYMsFplw5uJAbt++DX9/f3Ts2BH79u3je/lJkfLy8tCvXz8sW7YM77zzjtxxFIvl4kCmTJmCHTt2cFNKUiyj0YiePXuiefPmOHjwIPcOkxGXxRxEeno6kpKSkJiYyGIhxVq8eDEuXbqEgoICFovMOHNxAFevXoW/vz9efPFFbN++nZtSkiJlZ2dj+PDhWLNmDebMmSN3HMVjudg5URTx8ssv4/jx49yUkhSrpKQE/v7+6NKlC7Kysni+0QZwWczOff7559i9ezc3pSRFi4mJQWVlJTeltCEsFzt28eJFzJs3D9HR0dyUkhRr69atSEtLw+bNm9GuXTu549D/4bKYHRBFEcXFxaioqICbmxs8PT1RW1uLQYMG4dq1azh58iT3DiOH97Dj4MqVK/D398fw4cORlpbG8402hDMXG1ZaWorExESsXbsWFy9evP9xHx8fdO7cGYcPH8YPP/zAYiGH9qjjwNvbG05OTnBxcYFer2ex2BiWi43KysrC2LFjYTQaH/jcxYsXcfHiRTg5OaG8vFyGdETW8bjjoLCwEADg7OyMvLw8BAcHWzsePQaXxWxQVlYWQkNDIYoiamtrH/k4QRCgUqmQkZHBA4scTl2PA5VKBUEQeBzYGJaLjSktLUW7du1gMpkee0Ddo1KpoNFocPnyZbi7u1s+IJEV8Diwf3zPno1JTEyE0Wis0wEF/PdmSEajEUlJSRZORmQ9PA7sH2cuNkQURfj6+qKwsBD1+bEIggBvb2+cP3+eJzXJ7vE4cAwsFxty8+ZNeHl5Ner5np6eEiYisj4eB46By2I2pKKiolHP5zvHyBHwOHAMLBcb0tjrVZo3by5REiL58DhwDCwXG+Lp6QkfH596rxcLggAfHx94eHhYKBmR9fA4cAwsFxsiCEKDtwqfO3cuT2KSQ+Bx4Bh4Qt/G8P39RDwOHAFnLjbG3d0d6enp96++f5x7VyZ/9dVXPKDIofA4sH8sFxsUHByMjIwMaDQaCILwwDT/3sc0Gg12796N4cOHy5SUyHJ4HNg3louNCg4OxuXLl7F69Wp4e3v/6nPe3t5YvXo1ioqKeECRQ+NxYL94zsUOiKKIW7duoby8HM2bN4eHhwdPWpLi8DiwLywXIiKSHJfFiIhIciwXIiKSHMuFiIgkx3IhIiLJsVyIiEhyLBciIpIcy4WIiCTHciEiIsmxXIiISHIsFyIikhzLhYiIJMdyISIiybFciIhIciwXIiKS3P8DEdwYRaJWjukAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(mask=True, beta=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1e5b8732",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(mask=True, beta=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e788b91",
   "metadata": {},
   "source": [
    "Remove insignificant neurons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ed4800ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2 = model.prune()\n",
    "model2(dataset['train_input']) # it's important to do a forward first to collect activations\n",
    "model2.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61c8eeb1",
   "metadata": {},
   "source": [
    "Resize the figure using the \"scale\" parameter. By default: 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5cb8d57e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot(scale=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "67305f39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 200x160 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot(scale=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "51c722ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot(scale=2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03d4bf1b",
   "metadata": {},
   "source": [
    "If you want to see sample distribution in addition to the line, set \"sample=True\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c6d24148",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2(dataset['train_input'])\n",
    "model2.plot(sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3fa482a",
   "metadata": {},
   "source": [
    "The samples are more visible if we use a smaller number of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3856bcb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2(dataset['train_input'][:20])\n",
    "model2.plot(sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fa7ca2c",
   "metadata": {},
   "source": [
    "If a function is set to be symbolic, it becomes red"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3d502880",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best value at boundary.\n",
      "r2 is 0.9928952974445153\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor(0.9929)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.fix_symbolic(0,1,0,'x^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f8f93b9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e75a0760",
   "metadata": {},
   "source": [
    "If a function is set to be both symbolic and numeric (its output is the addition of symbolic and spline), then it shows up in purple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "17df5fed",
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.set_mode(0,1,0,mode='ns')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b5b13363",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LqKqqwooVK+B2uwEgrLUiSRIAwGw2Y+PGjaisrNSljkSRiuFCNIKqqiosXboUQggoinLJ75NlGZIkYfPmzQwYovMwXIgu4HQ6kZubC4/Hc9lgGSLLMkwmE5qbm9lFRnQOB/SJLrB27Vq43e6rChYAUBQFbrcbb7/99ijXjCh6sOVCdB4hBIqLi3Hy5MlrmhEmSRIKCwtx/PhxdTyGKJ4xXIjO09nZiaysrBG/Nguz0IAGGGFEN7oRQGDE8zMyMka7mkQRz6h3BYgiSU9Pz4jl8rke5FSkYgZmwAwznHCi/dz/OtABL7xwuVwMFyIwXCjOeb1e7N+/H7t27UJ1dTV279494vcpULAP+wAA7WhHNrLhgAM5yEEJSgAAfejDyXdPQswRyJqehRRHCrvIKG6xW4ziSl9fH/bs2YOamhpUV1fj22+/hd/vR1paGubMmYOKigr87ne/Q0tLy1X/TBNMcMCBaZnTsPqR1XCecgIAzJlmOEodyJqeBcd0B1InpjJsKG6w5UIxraurC9XV1eqfQ4cOQVEUOBwOzJs3D8uXL0dFRQWmTZsGWR7s+lIUBc8888xVD+h74EGT1IRnf/Us7nv6PvhcPnQe6UT7oXa0H2rHqS9PQSgCSalJatA4Sh2wFdggGzhhk2ITWy4UU5qbm1FTU6N2cx0/fhwAkJ+fj4qKCvVPQUHBJVsRWr/nEvQG0Xn0XNjUtaPr+y6E/CEkmBKQOS0TjtLBsLEX22FIMNzQv58oUjBcKGoJIVBfX4/q6mrs2rULNTU1OH36NACgpKQEFRUVmDdvHubOnYucnJxr+tnX+ob+li1bsGTJkqv62aFACN3Hu9Fe146Oug501HUg4AnAkGBARkmG2pWWOTUTCaaEa6o3UaRguFDUCIVCOHz4cFg3V2dnJ2RZxowZM9RWyZw5czSZsXW1a4t98MEHVx0sIxGKQE9DDzrqOtB+aDBwvL1eSLKE9KJ0tRsta3oWkqxJN/aPIhojDBeKWH6/HwcOHFCDZPfu3XC5XEhMTMTMmTMxb948VFRUYPbs2bBYLKNSB6fTibfffhu///3vL1oV+emnn8aqVauQlpam6d8phICrxaV2o3Uc6sBAxwAAIC0vbXiSQKkD5gyzpn83kVYYLhQx3G439u3bp3Zz7du3Dz6fDykpKSgvL1e7uW655RYkJY3tE/z5+7lYrVbY7fYxnfk10D6A9rp2tWXT19wHALCMs4SFjWWchTPSKCIwXEg3TqcTu3fvVlsmBw8eRDAYhN1ux9y5czF37lzMmzcPpaWlMBo5sfF8XqdXHbNpr2uH86QTQgiY7KawGWlp+WkMG9IFw4XGTFtbmxokNTU1OHz4MIQQGD9+fNjg+5QpU9RpwXR1/AP+wenP51o33ce7oQQVJFoSkXVTltqysRfZIRv5u6XRx3ChUSGEQFNTkxomu3btQkNDAwCgsLBQDZKKigrk5eXx6VpjQV8QXce61Hdtuo52IegLwphkRMbUDHX6c2ZJJgyJnP5M2mO4kCYURcGxY8fCZnK1trZCkiTcdNNN6kyuuXPnIjs7W+/qxh0lqKC7vjtsRpp/wA/ZKMNebB8Mm+kOZE7LRGJKot7VpRjAcKHrEgwGcejQobA1ubq7u2E0GvGDH/xAHS8pLy/nBloRSAiB3lO9YTPSPD0eSJIEW6ENjunDy9Yk25L1ri5FIYYLXRWfz4f9+/errZI9e/ZgYGAASUlJmD17ttoymTVrFsxmTo+NNkII9J/tV7vROuo60H+2HwCQmpuqjtk4pjuQ4kjRubYUDRguNKL+/n7s2bNHDZP9+/fD7/cjNTUV5eXl6jsmN998MxIT2Y0Si9yd7uEZaYfa0dvUCwBIyUpBVunwjDTrBCvHzOgiDBcCMLjAY01NjbouV21tLRRFQWZmpjr4Pm/ePEybNg0GAweA45HP5VODpr2uHT31PRCKQHJastqyyZqehfSCdEgywybeMVziVEtLixokNTU1+P777wEAEydODFvgsaioiE+lNKKAJ6AuyNlR1zG4IGcghARzwvD05+lckDNeMVzigBACJ0+eDJvJ1dTUBACYMmWK2iqZO3cucnNzda4tRauQP4Su413DM9IOdyDoDcKQaEDGlPOmP0/NhDGZL8XGOoZLDAqFQjh69KjaKtm1axc6OjogyzJKS0vVIJk7dy4yMzP1ri7FKCWkwNngDJsk4HP5IMkS7JPtajda1k1ckDMWMVxigN/vx8GDB9Ug2b17N/r6+pCYmIhbbrlF7eIqLy+H1WrVu7oUp4QQ6DvdFzZJwN05uOK0bZItbEaayW7SubZ0oxguUcjj8agLPFZXV2Pv3r3wer0wm80oLy9Xu7lmzpyJ5GS+o0CRSQiBgfaB4UkCh9rhOuMCAFjGW8K2GuCCnNGH4RIltm3bhr/85S+orq7GgQMHEAwGYbPZ1CVUKioqUFZWhoQEbi5F0cvT4wmbkdbb2Bu+IGepA7lzc7nVQBRguESJ3t5eKIoCo9GIhIQEGI1GGAwGPs1RTFOCCnwuH/wuP/z9g3/sxXaY0tltFukYLlFCURRIksQwobimhM5dB3yPJuIxXIiISHPc2IGIiDTHN5nOCYVC2Lt3L1wul95ViXo333wzHA6H3tWg6xAKhdBwtAE+j0/vqkS93KJcpKWn6V0N3bBb7ByPx4OlS5fC6/XCYrHoXZ2oNLQSwKuvvop77rlH7+rQdfD5fHjn+Xfg9/uRaOKCpNdDCAH3GTcWPLMAZXPK9K6ObthyOUcIAVmW8dvf/hbz58/XuzqjLhQKwe/3w2AwaLaqcSAQwKOPPgo+r0QxAQhJ4Pb/dzumlE3RuzZRwdfnw0DHAKzjrUgwJSAYCmL9b9YDcX4ZMFwuYDQakZQUG0tRCCHg8XjQ19eHtrY2NDc3o6GhAfX19Th16hRaW1uRkZGB5557DnfeeecN71vP2Wyxw2gw8p2pqyCEQNP+Jux7Yx9SslKQOTUTJctLeB2A4RKzQqEQNm7ciNdffx2tra1wuVzw+/0XtSqOHz+Op556Cn/6059w880386IguhYCaPuuDYpfgavFBU+3B5Pvn6x3rSICZ4vFICEEqqqq8MILL6C2thadnZ3w+XyX7K7q7OzEmjVr4Pf7x7imRNHNP+BH17Eu9diaY4VlHMdsAYZLzBFC4JtvvsEvf/lL9PX1XfR1o9EIi8WCiRMnhu1tv23bNnz11VccL6GLCCHUPxSur7lPXXwTADJvyoQhiXvXAOwWiylCCDQ0NOCZZ57B2bNn1fKysjLcddddKCwsRH5+PsaPHw+73Y4tW7bgueeeQzAYhMfjwe9//3vMnTuXs+UIACAUAU+PB2f2nUHIH8KUpVMA9pqqhBBor2uH4lcGC2Qguyxb30pFEIZLjBBCoKurC8899xyOHDmilk+dOhVvvvkmCgsLLxpPeeCBB7B+/Xrs2rULALBnzx5s3rwZjzzyCMde4pwICXz3zndo2NYAT48HKVkpyLstj2t6nUcJKWivbVePk6xJsBfZdaxRZGG3WIzw+/3413/9V3z99ddq2bhx4/Diiy+OGCwAkJKSgtWrV8NkGrxhBINBvPrqq+jq6rroeynOyEAoEIKn2wMIYKBjAGe/PcuusfP4en1wNjjVY9skG5LTucXFEIZLDBgawN+4caN68VutVvzud7/DrFmzLtkKkSQJd9xxBxYvXqyWHT16FO+++y5vInFOkiTk35YPQ/K58QMBnPryFJSgom/FIoQQAj0ne+Dt9aplWaVZkI28pQ7hbyIGtLW14d///d/h8w0u2ZGQkIAXXngB99xzzxW7txITE7F69WqkpqYCGFx9+a233kJTUxMDJs7ZJtmQUZyhHncc6UBf88WTROJV23dtwNBwi1GGY7qD3cnnYbhEuVAohNdffx3ff/+9WrZw4UI8/vjjMBiuPGtFkiTMmDEDK1asUMuam5vx5ptvQlH4lBrP5AQZ+bfnq4P4QXcQzdXNfOgAEPKH0HG4Qz02ZZiQlhe/64iNhOESxYQQOHLkSFg3VkZGBp5//nl1HOVqGAwG/M3f/A3GjRunlq1fvx6HDx/mjSSOSZKE8beODxvEP73rNAIDAR1rFRkG2gfgahle5NZebEeihWuxnY/hEsWCwSBee+01dHd3Axi8Gfz85z9HWVnZNTXPJUlCYWEhVq1apZ7X3d2NV199FYEAbyTxzJRhwrhbhx86+pr70HmkM64fOoQQ6D7WjYB7+NrInpHNDcwuwHCJUkIIderwkKKiIqxateq61giTZRmPP/44ioqK1LItW7Zg9+7dcX0jiXeSLCH/9nx1oFqEBBq/bIRQ4vgzIYCz351VF6Y0JhuROTWT4y0XYLhEKZ/Ph1deeQUDAwMABru2/vZv/xbZ2df/Eld2djaeeuopdazG7XZjzZo18Hg8mtSZoo8kScgsyURqXqpadvbAWbg73Jc5K7YF3AF0fT88Xd8y3sIlX0bAcIlCQ62W899pKSsrw/Lly2/o6UmSJCxfvhy33HKLWvaXv/wFVVVVbL3EMaPJiLz5eeqxr9eHM/vOxO1noq+lDwMdA+px5tRMGJP5PvqFGC5RKBAI4A9/+IPaojAajXjqqafU6cQ3wmq1YvXq1eq2A4FAAK+88gqcTucN/2yKTpIkIXduLhIs55bgF4MD+/H4zosQAh11HcNLvkiD4y10MYZLlBFC4LvvvsOOHTvUstLSUtx9992a9PlKkoS77roLd955p1pWW1uL9957L26fVAmw5FiQOTVTPe5p7MFA+8BlzohNQhFoq21Tj5OsSbBPtnO8ZQQMlygTCoWwdu1adaxFlmU88cQTsFqtmv0dycnJWL16tbqApaIo+K//+i+0trZq9ndQdJENMnJuzVGPA/0BdBzuiLsHDm+vN2zJl9T8VJgyuN7aSBguUUQIge+//x6ffPKJWjZ58mQsXbpU0ycnSZIwa9YsLFu2TC1rbGzEH//4R75YGackSYKjzAGj6dzYggDO7j8bV7PGhBBwNjjhdQ4v+ZI9PZtLvlwCfytRRAiBdevWqeMfkiThJz/5Cex27VdiNRqN+Lu/+ztkZWWpf/c777yD48ePx93TKg2yZFuQOnF4XK/rWBf8rvjaYK69th0iNPj5lwwSskqzdK5R5GK4RJHGxkb83//9n3qcl5eHhx56aFT6eyVJwpQpU/CTn/xELWtvb8frr7+OUCik+d9Hkc+QZICjzKEeu7vccDY69avQGFMCCtoPDy+xb8owwZZv43jLJTBcooQQAuvXr0d7+/CH+5FHHglbskVrsizjySefxKRJk9SyTZs2Yd++fWy9xKlxM8ZBMgzeTEVocHA7Xj4LAx0D6Ds9vHCnvciORCuXfLkUhkuU6OzsxIcffqgeZ2dnY+XKlaP+1JSTk4O//uu/Vt/67+/vx8svv6yuwEzxQ5Ik2ArC9yzpqOuIiynJQgh0He8KW1eNS75cHsMlCgghsH37djQ2Nqply5YtQ15e3qVP0ogkSXjkkUdQWlqqlu3cuRNffvll3Dyx0rCk1CSkF6Srx32n++DpioMVHATQ/l27uuSLIdnAJV+ugOESBXw+HzZs2KDO1DKbzXj44YfH7INts9nwi1/8AgkJCWp93nrrLbZe4pAkS2HjLj6XDz31PTH/oBHwBNB5tFM9tmRbYM3Rbvp/LGK4RDghBGpra7F37161rLy8HKWlpWMWLpIkYcmSJZg5c6ZatmvXLi5qGYckSULWtCzIieduHQJoO9R2+ZNigOuMK+ylUS75cmUMlwgnhMD7778Pt3twoUCDwYCVK1ciMXFsBxJTUlLwV3/1VzAaBy8oj8eDN998k0vyxyFrrhXmTLN63HmkE0FfUMcajS4hBDqOdCDkOzdLcmjJF/aIXRbDJcKdPXs27KXJ/Px8LFy4cMz7eiVJwuLFi1FWVqaWffHFF9i/fz9bL3Em0ZwIe/Hwu1WuVhcG2mJ3KRihiMHxlnMSLYP/fo63XB7DJYIJIVBVVRW27MqyZcuQkZFxmbNGj9Vqxc9//vOwJfnfeustBIOx+9RKI5CA7LLhJ/egJ4iuY10x+5Dh6/Ohu75bPU7LS4M5w3yZMwhguEQ0t9uNDRs2qBdtamoqli9frlt9JEnCvffei2nTpqlln332GWpra2P2xkIXkyQJGSUZw2MOYvDNdcTgR0AIAWejE96e4SVfsqZnQU7grfNK+BuKUEII7N+/H7W1tWrZ/PnzMWXKFF2b42lpafjZz34W9t7LH/7wB761H2cs2RZYxg9vkNV1rCts299Y0n4ofMkXR6njCmcQwHCJWIqiYP369fB6B5+YjEYjHn30UXVAXS+SJOH+++/H5MmT1bJPPvkER44c0bFWNNaMyUZklgwvwT/QMQDXGZeONRodSkBBx6EO9Tg5PRm2SVzy5WowXCJUU1MTPv/8c/V4ypQpmD9/fkR8qDMyMvD444+rdent7cXatWvZeokzjjKHOu6i+BV0Hu2Mue5Rd5cbvad71WN7kR1JqUk61ih6MFwikBACmzdvRmfn8Etby5cvR1pamo61Gja0HXJBQYFa9vHHH+PEiRM61orGkiRJsE+2I9EyPCW+/VB7TC3BL4RA23dt8PcPr/zsKHNwyZerxHCJQC6XCxs3blSfAjMzM/HDH/4wIlotQ7Kzs/HjH/8YkiRBkiSYTCY0NzfrXS0aQ+YMM6y5w2+pd9d3w9cXO6s2hHwhNO5oVCcqGE1GZJdlR9R1GMkYLhFGCIFdu3bh6NGjatnChQvDViaOBJIk4Uc/+hHmzp2Lf/zHf8TmzZtx11136V0tGkNyggzHTectwd/pjpmusaGFKruOd6llWdOzwvazocvj+gURJhgMYv369eqb70lJSVi5cqX6bkkkycnJwbvvvouUlBRIkgS/P742jiIgZ3YOvv/4eyh+BVCA5upmTCifoC7LH62EInDy85OD/y4MzhIrXFzIXSevAX9TEUQIgfr6enz11Vdq2fTp0zFr1qyIbIpLkgSLxRKRdaPRJ0kS0gvSkZo7/DTfVtsWtg1wtOpv60frvuGXl1NzU5F9M7vErgXDJcJs2rQpbBvjhx9+GCkpKfpWiugSjCYjcmbnqMeeLg866jqiumtMCIHTX5+Gr3d4/Cj/znwkpnBjsGvBcIkg3d3d2LRpk3o8btw43HfffXxaooglSRJyZ+fCkHSu21YAp6tPR/WsMf+AH41fNKrHSWlJyJufx+vwGjFcIoQQAl988QUaGhrUsiVLliAnJ+cyZxHpLzU/FWn5w9PkO+o6onYDMSEE2g62wdUy/EJozqwcpGSz9+BaMVwihN/vx4YNG9QXEU0mEx555BE+LVHEMyYZMaF8gnrsdXoH33mJwq4xJajg5LaT6nIvcqKMgkUFfLflOjBcIoAQAkeOHEFNTY1aNnPmTMyYMYPhQhFPkiTkzMoJW8gyGrvGhBBwNjjRUTe83EvGlAxkFGfwOrwODJcIIITAxo0b0d/fDwCQZRmPPPIIkpOTda4Z0dVJzU2FrcCmHnce6YS7w61fha6HABp2NiDoObeFhAQULCoYHk+ia8JwiQDt7e3YvHmzejxx4kQsXryYT0sUNQyJBkyYO9w15uvz4ezBs1HVNebp9qC5eniViZTsFOTcmsPr8DoxXHQmhMBnn30WtnTK0qVLkZWVpWOtiK6NJEkYP3M8jObhrrHm6mYoIUXfil0lIQSadzeHTUTIm5+HZBt7D64Xw0VnHo8HGzZsgKIMXoRWqxUrVqxQ90shihapE1JhLxre/rjrWFfUbH8c9AbRsL1BXUcsISUB+Xfm61upKMc7mI6GNgT79ttv1bKKioqwnR6JooVslJE7N1ddht/f78fZbyO/a0wIgY7DHXCedKpl2TdnI3ViKrvEbgDDRUeKomDDhg1hG4I99thjSEhI0LlmRNdOkiSMu2UcElLOfX4F0Ly7GUowsrvGhCLQ8HmDWk/JIKFwUSFkA2+PN4K/PR01NTVh27Zt6vHkyZNx++2382mJopZlnAWZU4Z3qOw63hXxO1S6Wlw4e+CsemybZIOj1MHr8AYxXHQihMBHH32E9vZ2teyhhx6KmA3BiK7HhV1jwYEgWve3RmzXmBACjV82wu86t6K3BExaOAlGExeMv1EMF504nU6899576nFmZiYeeOABPi1RVJMkCdk/yEaSdXgr4JbdLVACkdk15uvz4fTXp9Vjk92E3IpcXocaYLjoQAiB7du34/jx42rZkiVLIm5DMKLrYc4yI2Nahnrcc7IHfc19OtZoZEIItH7TClfrcLfdhPIJSMnkOmJaYLjowOv1Yt26dWHriD322GOcfkwxQTbImDh34nDXmCeIM/vORFzXmBJQBqcfn2tUGZINKLirQK033RjezcaYEAI1NTXYu3evWlZeXo5bbrmFTXGKCZIkwTHDEfYCYvPuZoR8IR1rFU4Iga4TXeg82qmWZU7NRHphOq9DjTBcxlggEMAf//hHdfpxQkICVq1ahaSkpCucSRQ9zBlmZN00vMpE76le9Db16lijcEIRaNzeOBx4MganHyfwlqgV/ibHkBACBw8exBdffKGWlZWVYeHChXxaopgiyVLYrLGQL4QzeyOna8zd4UbLnhb1ODUnFeNuGcfrUEMMlzEUCoWwdu1aDAwMLokhyzKeeOIJWCwWnWtGpC1JkuAoc8BkN6llLftaEPQGdazVICEETu86Da/Tq5bl3ZGHpFT2HmiJ4TJGhBA4duwYqqqq1LLi4mLce++9fFqimJRsS4aj1KEe9zb1wtno1L31EnAHBrcxPleNxNRE5N3GbYy1xnAZI0IIrFu3Dj09PQAGn+x+/OMfw263X+FMougkyRJyK3LVu4ziV9Cyu+XyJ40yIQTaatvQe2p4/Gf8zPGw5lh1rFVsYriMASEEDh8+jI0bN6plEydOxEMPPcSnJYpZkiQh66YsmDPNatmZfWeGN+PSgRJU0LCtYXgb4wQZhYsKuY3xKGC4jIFAIIA1a9agq6sLwOBFt3LlSowbN07nmhGNruS0ZGTPyFaPXWdc6K7v1q1rrO90H9pq29Tj9KJ0ZEzlNsajgeEyyoQQ+OKLL/Dpp5+qZUVFRVi1ahU/0BT7JAwup2IY/KwrAQUtNfp0jQlFoGFHA4Lu87YxvqsAxiSuIzYaGC6jzOVy4cUXX4THM7jDndFoxOrVq5GdnX2FM4minyRJyCzJRIpjeEmV1m9b4R/wj3ldPE4PmncN7/hqzjJjQvkEPuSNEobLKBJC4P3338c333yjls2ZM4cLVFJcSbImYdwPhruAXa0udB8b264xIQTO7D2DgY7hnTEnzpsIU7rpMmfRjWC4jBIhBFpaWvDaa6+pa4iZzWY8++yzSEnhwngURyQgd+5w15gICpz+y2kIZezCJegLouHz4W2MjWYjJi2YxHXERhHDZZQoioL//M//RGNjo1q2bNkyzJs3j60WiiuSJME+xQ7r+OHpvqe+PoX2Q+1j0noRQqDr+y5013erZY5SB9Ly0ngtjiKGyygQQqC2thb/+7//q5Y5HA6sXr0aRiMHDyn+JKYkIn9B/vBKye4gDvz3Afh6faMeMOo2xv4LtjE28vY3mvjb1ZgQAt3d3fi3f/s3OJ1OAINPbk8++SSKi4v5pERxSZIkFN9XjMxpw1sg99T34MDaAwh6gqMWMEII9Db1ovWbVrUsLS8N2TOyeS2OMobLJYRCIRw4cABut/uqzxkKlmeffRY7d+5Uy6dOnYpVq1ZxvxaKa4mWRPxg1Q+QYEkYLBBAw+cN+Pa/v0XQp23ACCHg6fHgyAdH8NVvv4Kvzzf4BQnIvzMfCSkJmv1dNDLe7Ubg8XjwyiuvYMWKFXjjjTcQDF75jeKhYHnmmWewZcsW9UIxm8345S9/iaysrCv8BKLYJkkSMqdmYvqPpg93SQmgvqoeB9ceRMgXuuGAEULA2+vFsY+PYdsL23Bw7UEMtA/PEEu2JSNvPtcRGwscALiAx+PBP/3TP+Hdd99FMBjESy+9BIfDgcceewwGg2HEc84Plk8++SQsWP75n/+Zi1MSnSPJEqb8cAr8A34c2XhkcBkWBTjxyQn4+nwo+WEJ0ovSIRvlq75mhBAQioDX6UXLnhYc+/Mx9J3uU2eGDUm0JuKmh28Ke+eGRg/D5QJGoxHJycnq9GG3241/+Zd/gSzLePDBB5GYmAhZDv/gd3V14ZlnnsGnn34aFiy/+tWv8OSTT3IQn+g8hgQDSleWQoQEjm46ChESECGBpi+b0LK7BY5SBybfOxnZZdkwmowjhsz5gdJR14Hm6ma017UPLqN/QagYzUbk3ZaHkh+WDM4Q4zpiY4J3vQskJCTg+eefx6lTp7B161YAQH9/P1544QW88cYbsNlsSE9PR0ZGBjIzM2G327F9+3bs2LEjLFh+/etf42c/+xmDhWgEhkQDSh8rhRJScOzjY+pCkiFfCK3ftOLsgbNIL0jHxNsmIik1CbJBhiRLkAwSREigr7kPncc60dvYO2KgAIDRZETunFyUPFACW4Ft8Hz2IIwZ3vlGkJaWhhdffBG/+MUvsGPHDgCDLZjDhw9f8VwGC9HVMSYZMeOnM2DOMuPElhNwnXGpISFCAt0nutF9ojv8JAkjBsn5DMkG5Nyag6kPToW92M5Q0QnvfiOQJAkOhwMvv/wy/v7v/z5sW+LLMZvN+M1vfoMnnniCwUJ0FYxJRpT8sAST7pyElr0tqK+qR8+JHihBZeQTLhEscqKM1ImpmDBrAibMmQDbJNs1jduQ9ngHvARJkpCdnY3XXnsNb7zxBurq6tDT04O+vj709/fD4/HA7/cjEAhAURRYrVb86le/wuOPP85gIboGkiQhOS0ZhYsKkXdbHjoOdeDEpyfQ9l0bgr7giIEiyRISLYlIzU2Fo9SBnNk5SMtPgzFp5DEaGnu8C17GUAvm17/+NRRFQTAYRCAQgNfrxcDAAFwuF5xOJ/r6+jBhwgSUlpZeckYZEV2eJElISE7A+FvHI/vmbLjOuODt8UIJKRCKGPzvubGZZFsyLOMsg+Mx56Y1M1QiC8PlPIqiYO/evdf04iQAyLKM1tZWtLa2XvmbY1gwGFS3caYoJoBTR0/B7x37ZfEvS4J6x+rt70XbibbLfrtelJACr8urdzV0x3A5R5ZlTJ06Fdu2bcO2bdv0rk7UslqtSEtL07sadJ1kWUZaXhrO7DuDM/vO6F2dqJVkTkKyJVnvauhKEnrtNxphhBAIBkdvjaN4YjQaudRNlBJCIBS68TflCTAYDHF9HTBciIhIc/Ebq0RENGoYLkREpDmGCxERaY7hQkREmmO4RAnOZiMafIfEP+CHErrE8jAUMRguUaK2thbjxo1DbW2t3lUh0o2z0Yn3V74PZ6NT76rQFTBciIhIcwwXIiLSHMOFiIg0x3AhIiLNMVyIiEhzDBciItIcw4WIiDTHcCEiIs0xXIiISHMMFyIi0hzDhYiINMdwISIizTFciIhIcwwXIiLSHMMlCggh0NPTA0VR0NPTwz1dKC4JIdDT3QOPx4Oebl4HkY7hEsGcTifWrFmD4uJiLFiwAD09PViwYAGKi4uxZs0aOJ1OvatINOrOvw5ml8/G9u3bMbt8Nq+DCCcJxn9EqqqqwooVK+B2uwEg7ClNkiQAgNlsxsaNG1FZWalLHYlG24XXgU3YcC/uxSf4BE7JCYDXQaRiyyUCVVVVYenSpfB4PBBCXNT8HyrzeDxYunQpqqqqdKop0ejhdRDd2HKJME6nE7m5ufB4PFCUK+8TLssyTCYTmpubYbPZRr+CRGPgUtdBOtLVlksPetRyXgeRhy2XCLN27Vq43e6rChYAUBQFbrcbb7/99ijXjGjs8DqIfmy5RBAhBIqLi3Hy5MlrmgkjSRIKCwtx/PhxdTyGKFpd7jq4VMsF4HUQadhyiSBdXV2or6+/5imWQgjU19eju7t7lGpGNHZ4HcQGhksE6e/vv6HzXS6XRjUh0g+vg9jAcIkgFovlhs63Wq0a1YRIP5e7DvrQh0/wCfrQd8nv4XUQGRguESQjIwNFRUXX3F8sSRKKiopgt9tHqWZEY+dy10EIIfSgByGELvoar4PIwnCJIJIkYfXq1dd17tNPP81BTIoJvA5iA2eLRRi+50LE6yAWsOUSYWw2GzZu3AhJkiDLl/+/R5ZlSJKEDz74gBcUxRReB9GP4RKBKisrsXnzZphMJkiSdFEzf6jMZDJhy5YtWLJkiU41JRo9vA6iG8MlQlVWVqK5uRkvvfQSCgsLw75WWFiIl156CS0tLbygKKbxOoheHHOJAkIIdHd3w+VywWq1wm63c9CS4g6vg+jCcCEiIs2xW4yIiDTHcCEiIs0xXIiISHMMFyIi0hzDhYiINMdwISIizTFciIhIcwwXIiLSHMOFiIg0x3AhIiLNMVyIiEhzDBciItIcw4WIiDTHcCEiIs39fzv6jkNu8e+dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
